The Larrakia People lodged the Kenbi Land Claim under the Aboriginal Land Rights (Northern Territory) Act 1976 (Cth) on 22 March 1979. There were four separately represented claimant groups (totalling 1600 people) who claimed land available on the Cox Peninsula and the islands and reefs to the west of the Peninsula.

After 21 years, three hearings before the Full Bench of the Federal Court, three before the High Court, and two before the Land Commissioner, Justice Gray published his recommendations in a Report to the Minister for Aboriginal and Torres Strait Islander Affairs and to the Administration of the Northern Territory in December 2000.The Report rejected the claims of three of the claimant groups but found that the Tommy Lyons Group, which consisted of six people, fell within the statutory test of 'traditional Aboriginal owners' in the Act with respect to a substantial part of the claim. As such, it was recommended that most of the land claimed be granted to an Aboriginal Land Trust. The recommendation made it clear however, that all the claimants would benefit as they also had strong traditional interests to the land claimed.

The Land Commissioner's recommendation then went to the Federal Minister for Aboriginal and Torres Strait Islander Affairs, who, under the Land Rights (NT) Act 1976 (Cth) makes the decision to grant the land or not.

Chief Minister of the time, Denis Burke, opposed the proposal to return the 600 square kilometres of land to the Larrakia People and appealed the Land Commissioner's decision. The Northern Territory Government's appeal was ultimately withdrawn in 2002 with the election of the Martin Labor Government.